measurements and SI

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Transcript measurements and SI

Physics Tools and Standards
Each discipline has a language.
The language of physics is math!
What are the mathematical tools
you need to succeed?
Measurements
• We need a way to standardize
measurements
• Compare to a known quantity
• Must be constant, repeatable, and
agreed upon by all users
Measurements
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• Constant, repeatable,
agreed upon
• Divide into groups of 3
• What is the size of the
lab tables?
• What is the time it takes
for a pencil to fall from
the 2nd story to the
ground?
Measurements
• Was your data reproducible? How could you
test this?
• How did you agree upon the standard?
• Did you use estimates if your measurement
was not an exact number of your standard?
How did you estimate?
• How accurate were you? How could you be
more accurate?
Metric System and SI Units
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• Standard
measurements based
on powers of 10
• SI units standardized
and accepted by
scientists worldwide
• All your answers will
include the SI unit!
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Derived units are combinations of the base units.
Ex: speed is measured in meters per second or m/s
SI Prefixes
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How To: Converting Units
• Remember factor-label method?
• Multiply your quantity in one unit by a
conversion factor that =1 to convert to
another unit
• REMEMBER- units are your friend!
Keep them involved and you will
succeed.
How to: Converting Units
Ex: convert 10 m to cm
1. Draw a big T
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2. Put your starting number in the top left and its same unit in
the bottom right
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How to: Converting Units
3. Write the unit that you want in the top right
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4. Add numbers to your conversion factor to make it =1.
(how many cm in a m or vice versa)
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How to: Converting Units
5. Multiply through and cross out units that cancel out.
*** You can do these conversions in multiple steps***
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Practice Problems
p. 7 #5-8
UNITS ARE YOUR FRIEND!!!
Treat units as algebraic quantities in your
calculations and keep them superglued to
their numbers!
When you do this and the units of your
answer are correct, then your answer should
be as well.
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Scientific Notation
• Really big or really small numbers can be a
bummer to write and work with
• You can get either really big numbers by
using positive powers like 1 x 105 = 100 000
• You can also show really small numbers by
using negative powers like 1 x 10-5 = 0.00001
• Don’t worry about using your calculator to
figure out what these mean- just move the
decimal point left (negative exponent) or right
(positive exponent) the number of spaces
given by the exponent
The Power of Powers
• Powers of 10 used in scientific notation
mean big differences in the value of a
number
• For example:
• 106 sec is about 12 days
• 109 sec is about 32 years
• 1012 sec is about 32000 years!
How to Read Scientific
Notation
Now try 2 x 10-9
How to Write Scientific
Notation
1. Move decimal so only 1 nonzero # is to the
left of the decimal
2. Count how many spaces you moved the
decimal- if you moved right the exponent is
negative and if you moved left it is positive
3. Get rid of any nonsignificant digits (more on
this later)
4. Write the number multiplied by 10 to the
power of however many spaces you moved
in step 2
Practice Problems
1. Write the following numbers in scientific
notation.
a. 1.156
b. 21.8
c. 0.0068
d. 27.635
e. 0.219
f. 444
2. Write out the following numbers in full with
the correct number of zeroes.
a. 8.69x104
b. 9.1x103
c. 8.8x10-1
Scientific Notation and
Calculators
• On your calculator,
scientific notation is
often shown using
the letter “E”
• So 9.2 x 10-4 would
be written 9.2 E -4
• To enter a number
look for the EE or
Exp key
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Try it on your calculator
• To check yourself, multiply 6.0 x 105
times 4.0 x 103 on your calculator. Your
answer should be 2.4 x 109.
Accuracy and Precision
No measurement is perfectly
exact!
Precision
• Degree of exactness
• Written as +n ex:
40.1+1mm
• Increase precision by
finer divisions of the
scale
• This meter stick has
divisions down to the
mm so you can be
precise to 0.5mm
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Accuracy
• Are your measurements correct?
• Calibration checks measuring tools
against a standard
Significant Digits
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• Valid digits in a
measurement
• Depends on the scale
used
• Using top ruler, we are
certain of 2.5 and are
guessing 2.55 so 2 sig
digs
• Using the bottom ruler
we are certain of 2 and
are guessing 2.5 so 1
sig dig
Sig Digs
• What if your measurement falls exactly
on the line of 2.5mm?
• Record it as 2.50mm because you are
certain to within 0.01mm
Sig Digs: the rules
•
•
•
•
Nonzero digits always sig
Final zeros after a decimal pt always sig
Zeros btwn other sigs are always sig
Final zeros that are not after a decimal
pt are unknown– 3400 could have 2,3,or 4 sig digs
– Write it in scientific notation to clarify
Working with Sig Digs
• RESULTS NEVER HAVE MORE SIG
DIGS THAN YOU STARTED WITH
• Do the math first:
– Add/subtract: perform operation and then
round to lowest decimal sig figs that you
started with
– Multiply/divide: perform operation and then
round to lowest total sig figs that you
started with
Write 4 numbers on a piece of paper and trade it with your
neighbor- decide how many sig digs
The bottom line on sig digs:
Don’t write out everything your
calculator displays!!! Your answer
should only include the sig digs.
Review
• You have 2 measurements: A=1.24m
and B=0.23cm
– Which has more sig digs?
– Which is more precise?
Review
• You put your backpack on a scale and
find that it weighs 14.2kg. What is the
range of weights implied by this
measurement? How would you write
that?
• 14.2+.05kg (1/2 of the smallest division
of measurement)
Graphs
•
•
•
•
Remember the basics of experiments?
Independent variable is manipulated
Dependent variables change as a result
Graph independent vs dependent
Linear relationships
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• y=mx+b
• Slope=m= y/ x
• Remember + slope
is up to the right,
• -slope is down to the
right
Nonlinear relationships
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• Quadratic- when
one variable
depends on the
square of anothery=ax2+bx+c
• Inverse- when y
variable depends on
1/x
Practice: graphs
• Practice problems p. 18 # 24